查询词典 defect subspaces

In an infinite dimensional space there always exist two subspaces whose vector sum is different from their span.

在一无限空间中恒存在两个子空间，其矢量和与其张成空间不同。

We first analyze the relationship between the characteris-tic subspaces of linear transformation A,and its conjuge transformation A*, on then-dimensional complex inner product space Cn, and prove that the characteristicsubspace of an enginvalueλof A is orthogonal to that of enginvalue μ of A* if λ≠μ.

首先，分析n-维复内积空间Cn上的线性变换A与其共轭变换A*的特征子空间之间的关系，证明出只要A的一个特征值λ与A*的一个特征值μ的共轭不同，那么它们对应的特征子空间是正交的。

Equivalently, it can be raised as follows: for an A operator T, if M and N are two invariant subspaces of T satisfying N include M and dimN/M=∞, then does there exist another invariant subspace L such that N include L, and L include M ? It is rather difficult to study the invariant subspace problem of general diagonal operators.

研究表明它可以约化为对角算子的不变子空间的情形，具体地它有如下的等价提法：对于A算子算T，，如果M和N是T的两个不变子空间，满足且dimN/M=∞，那么是否存在T的另一个不变子空间L使得M包含于L，且L包含于N？

It is proved that every Lie derivation of nest algebra is the sum of an associative derivation and a general trace. Every Lie isomorphism between nest subalgebras of a factor von Neumann algebra is the sum of an isomorphism and a general trace or the sum of a negative anti-isomorphism and a general trace. Lie invariant subspace of linear mappings on Banach algebras is introduced, and linear maps from nest subalgebra of a factor von Neumann algebra into itself which satisfy the property that the space of derivations is their Lie invariant subspaces are characterized. Simultaneously, it is shown that such maps are Lie derivations modulo the set of scalar multiple of the identity.

得到Lie导子的特征表示，即套代数上的任何一个Lie导子都是内导子与广义迹之和；给出了Lie同构和同构及反同构之间的关系，即因子von Neumann代数中套子代数之间的任何一个Lie同构要么是同构与广义迹之和要么是负反同构与广义迹之和；引入了Banach代数上线性映射的Lie不变子空间，并给出von Neumann代数中套子代数上以导子空间为Lie不变子空间的线性映射的一个刻画，同时也表明在模去数乘恒等映射的意义下，以导子空间为Lie不变子空间的线性映射就是Lie导子。

According to the fact that the sum of linear subspaces, each of which is spanned by the rows of all points in each image, is equal to the linear subspace spanned by the rows of space points, projective depths are estimated.

深度因子则根据每幅所有图像点构成的行向量生成的线性子空间和与射影重建空间点构成的行向量生成的线性子空间是同一线性子空间的特性被估计出来。

A neural network architecture, K-subspaces and time-delay auto-associators, is proposed for phoneme recognition. It extends the phoneme filter neural networks approach by adding linear auto-associators to create p-dimension subspace, and an iteration is employed to improve the decision.

提出了用于音素识别的K子空间和时延自相关器神经网络结构，用将时延设计加入线性自相关器，以扩展音素滤波神经网络的方法，产生p维子空间，并采用迭代过程修改划分，以便捕获语音信号中的时间序列信息。

First,the feature subspaces are formed from different pose images using ICA and PCA.Then the pose image is transformed into its corresponding frontal face image using the transformation matrix predetermined by learning.Based on this foundation,the wavelet transform is applied to face images,and the authors compare the frontal face feature coefficients directly which are obtained by using the transformation matrix with the feature coefficients of the original face images,the recognition rate is improved greatly.

首先利用ICA和PCA提取不同姿态人脸的特征子空间，然后利用通过训练得到的姿态转换矩阵合成其相对应的正面人脸图像，实验表明ICA人脸识别算法要优于PCA人脸识别算法，并在此基础上用小波对人脸图像进行预处理，据姿态转换矩阵得到的正面人脸特征系数直接进行分类比较，识别率得到了很大的提高。

More broadly, the effect of any orthogonal matrix separates into independent actions on orthogonal two-dimensional subspaces.

更广泛的说，任何正交矩阵的效果分离到在正交二维空间上的独立动作。

The detailed coefficients of DWT contain signal and noise. Instead of the soft-thresholding method, SVD is applied to decompose the signal features and noise into different orthogonal subspaces. With the reconstruction of the singular vectors in subspace, the signal features are extracted effectively.

该方法通过对每层小波分解细节系数进行奇异值分解，将其中的信号特征成分和噪声分解到不同的正交子空间中，在子空间中选取集成信号特征成分的奇异值矢量进行重构，从而提取出淹没在细节系数中的有用信号成分，最后进行小波重建，得到降噪信号。

Based on the array signal processing and the eigenstructure decomposition method, the signal subspace and the noise subspace are achieved by reconstructing and decomposing the data matrix collected by the array sensors. By using the orthogonal properties of the two subspaces, the information about the velocities and bearings of spatial moving targets can be exactly obtained.

本文提出一种超分辨的二维谱估计方法，它利用的是阵列处理技术，对天线接收数据进行本征分析，将信号数据张成一个空间并对其进行分解，根据正交原理分割成信号子空间和噪声子空间，构造出噪声本征矢量，利用信号子空间与噪声子空间的正交性，在空间谱上形成极值点，从而达到对方向和速度的二维高分辨率估计。

Don not attempt to do something which you can not to do.

不要企图做那些办不到的事情。

The expression of CTGF and TNF-αweredetected by immunochemistry and the number of Clara Cells was calculated.

光镜下观察肺组织的病理变化，采用免疫组化染色观察肺组织中结缔组织生长因子和肿瘤坏死因子-α的表达和Clara细胞的数量。